detection depth

[green]

Thanks for the test-coil info. I think that assuming coil diameter is the mean of the inner and outer diameters is going to be OK. What is potentially the tricky thing with these flat coils is the lack of mutual inductance between each turn. Which means the inductance will be less than a tight bundle would be. This will affect the smallest 133mm coil the most.
I've been struggling to work out how to analyse the measured data, do I use the original or corrected data, can I correct it a different way etc. What I was trying to find out, in particular, was the Z = 0 figure. It would be nice to end up with a straight-line plot of real vs theoretical data, that I could just draw a straight-line through and get the best fit relationship, and hence calculate a good 'measured' Z = 0 value. In the end, I settled for a non-graphical estimation.

You will be pleased to know that I've cracked the problem, for both fixed-inductance and ( I hope ) fixed turns. The fixed-inductance analysis matches the 133/200/300 test data pretty well: 133 vs 200, 200 vs 300, and 133 vs 300.

Plenty of synapses were damaged in the process.

When I've cleaned up my maths, I'll post up the 'recipe', so you can assess it yourself.

I hope you have cracked the problem. I've been working on a reply but will wait to see your reply first. Did a test awhile back correcting for inductance change.
http://www.geotech1.com/forums/showt...537#post203537

[Skippy]

First error: assuming V = -L * dI/dt was relevant. We're not passing a current through the coil on receive, so physics involving mutual coupling between currents in adjacent turns (which causes L to vary with Turns², not simply Turns) is not applicable. The voltage out of a coil is just proportional to the number of turns in it.
Second error: Varying the current I in the hyperphys calculation. This variation just gets squared (when we calculate Gauss² ) and makes things less clear. If I is kept constant, any additional corrections due to current/turns become easier.

I chose my hyperphys current to give 1.0000 Gauss at Z = 0, with the 200mm coil.

I thought about what changes would happen at Z = 0, when the coil size was increased from 200mm to 300mm, initially for fixed-inductance.

* The larger coil generates a weaker transmitted B : it is reduced to 2/3. The target receives this weaker excitation, and passes it on proportionally when it re-transmits.
* The larger receive coil will pick up less voltage from the target: the voltage will be reduced to 2/3. [ I struggled with this bit ... there are formulae out there for loop antennas that give a voltage output proportional to loop area when a constant magnetic field passes through the loop ... but that doesn't apply here, the field isn't uniform and constant, for one thing.]
* The number of turns on the receive coil is lower, the received voltage is reduced in proportion to the no. of turns. No. of turns is lower than the 200mm coil by a factor of Sqrt ( 2/3 ) [assuming 200 * T² = 300 * N² ]
* The transmitted current is effectively reduced in proportion to the number of turns, which are reduced by a factor of sqrt ( 2/3 ). Example: The 200mm coil has 1 Amp and 26 Turns, modelled as 26 Amps and 1 turn; the 300mm coil has 1 Amp and 21.2 Turns, modelled as 21.2 Amps and 1 turn. [21.2/26 is approx sqrt( 2/3 )]

So, in total: Voltage out of the 300mm coil is reduced by:

( 2/3 ) * ( 2/3 ) * sqrt ( 2/3 ) * sqrt ( 2/3 ) = ( 2/3 )³ = 0.296 = 1/3.38

Similarly, for the fixed-turns coil:

* The larger coil generates a weaker transmitted B : it's reduced to 2/3. The target receives this weaker excitation, and passes it on proportionally when it re-transmits.
* The larger receive coil will pick up less voltage from the target: the voltage will be reduced to 2/3.
* The number of coil turns is unchanged, so there is no received voltage change due to this.
* The effective transmit current is also unchanged. Example: 1 Amp and 26 Turns through the 200mm coil is still 1 Amp and 26 Turns on the 300mm coil, both modelled as 26 Amps through 1 Turn.

So in total, voltage out of the 300mm coil is reduced by:

( 2/3 ) * ( 2/3 ) = ( 2/3 )² = 0.444 = 1/2.25

Similarly, going to the 133mm coil results in voltage output increases:

fixed inductance: Voltage = ( 200/133 )³ = 1.5³ = 3.38 = 1/0.296

fixed turns: Voltage = ( 200/133 )² = 2.25 = 1/0.444

And from 133mm to 300mm, fixed inductance: voltage = 2.25³ = 11.39 = 1/0.0878

Comparison to measured data:

Using your 'corrected' data for the 133/200/300 coils, I made a provisional estimate for Z =0 values as:
133mm coil: signal = 12920
200mm coil: signal = 3440
300mm coil: signal = 1056

These have ratio's of: 133 to 200 = 3.75; 200 to 300 = 3.26; 133 to 300 = 12.23.

A pretty decent match. The uncorrected data may be better, I may try it out.

[Skippy]

So, to actually get some new charts:

Enter a current, I = 15.9155A into the hyperphys calculator. For the 200mm coil, this gives B = 1.000 Gauss at Z =0.

For Fixed-inductance: Calculate Voltage output = 12000 * Gauss² * (200/coil-size) [coil-size in mm diameter]

For fixed-turns: Calculate Voltage output = 12000 * Gauss²

Hope I didn't mess that up.

Note: the hyperphys maths isn't too complex, it's not hard to put the formula direct into an Excel spreadsheet. The details of the mu, 4*pi stuff are irrelevant, as we're just tinkering with the output afterwards, anyway.

[green]

So, to actually get some new charts:

Enter a current, I = 15.9155A into the hyperphys calculator. For the 200mm coil, this gives B = 1.000 Gauss at Z =0.

For Fixed-inductance: Calculate Voltage output = 12000 * Gauss² * (200/coil-size) [coil-size in mm diameter]

For fixed-turns: Calculate Voltage output = 12000 * Gauss²

Hope I didn't mess that up.

Note: the hyperphys maths isn't too complex, it's not hard to put the formula direct into an Excel spreadsheet. The details of the mu, 4*pi stuff are irrelevant, as we're just tinkering with the output afterwards, anyway.

The reply I was working on. (distance vs amplitude_13) is the top part of (distance vs amplitude_8. For fixed-turns, I think is the same as you are suggesting. For fixed inductance , we got there a different way but the answer is the same. We put(200/coil-size) [coil-size in mm diameter] in a different place in the calculation.

The problem I have is

Here are the curves I have used for many years. The range reaches a maximum when it is equal to the radius of the coil. Coils larger or smaller than this optimum will result in less range

The curves assume that the number of turns and the coil current is the same in all cases; From description in link http://www.geotech1.com/forums/showt...517#post241517

[Skippy]

I've never really investigated Eric 'semicircle curves' , as to a VLF guy, they may not be relevant. Having now considered them hard, they don't seem to make sense.
However... the DO seem to match out 'fixed-inductance' simulation. Look at the excel data, for example the 400mm coil, at Z = 200mm. Note the output value, and see how at the same distance, the 300mm and 500 mm coils both give lower output.

In more mathematical detail:

We worked out: Output = Constant * Gauss² * (200/diameter)

Take the 'Gauss formula' and strip out the constants:

Gauss is proportional to R² / (Z² + R²)^1.5

Hence Gauss² is prop. to R⁴ / (Z² + R²)³

And the (200/diameter) term means output is proportional to ( 1/R )

Hence our total output is prop. to ( 1/R ) * Gauss²

or: Output is prop. to R³ / ( Z² + R² )³

I'm introducing a 'scale-factor' of 8 to make the numbers pretty, so:

Output = 8 *R³ / ( Z² + R² )³

Try it on the 400mm coil:

R = 0.200 At Z = 0, Output = 1000

At Z = 0.200, Output = 125

Now increase R: let R = 0.21; Output = 124.55

Decrease R: Let R = 0.19; Output = 124.51

Both figures are lower, (and roughly symmetrical)

[ It's worth noting : At distance ( Z = R ), Output = (Z=0 Output) / 8
it works pretty well for your real 133/200/300 test data]

And just fer fun, I've gone through the proper processes, and differentiated the output formula; when it is Zero (ie. slope is horizontal), it does occur when Z = R

I don't know whether our 'fixed-turns' simulation is correct or not, I can't think of any simple test that may verify it. However, I may be able to come up with some maths that shows where that data gives optimum coil diameter.

[Skippy]

Here's how to do it without charts: fixed-inductance

Output V =8 * R³ / ( Z² + R² )³ = (( 2*R ) / ( Z² + R² ))³

Suppose a 200mm diam. coil can just detect a target at Z = 200mm. With these Z & R figures, V = 64. This is the smallest V we can detect.

So with out new coil, at Z = R, we need V = 64.

Hence V_z=0 = 8 * 64 = 512. [ as mentioned previously]

Putting this in the above formula:

8 = ( 2*R ) / ( R² ) = 2 / R

hence R = 1/4 = 0.25 metres

A quick check with Z = 0.25, R = 0.25, gives V = 64, hence correct.

Try it with the excel data: the 95.96 value appears in [200mm coil, Z = 200mm], and [500mm coil, Z = 250mm] boxes.

[green]

For Fixed-inductance: Calculate Voltage output = 12000 * Gauss²* (200/coil-size) [coil-size in mm diameter]

For fixed-turns: Calculate Voltage output = 12000 * Gauss^{2 (from reply #168}

^{Coil diameter is just one of the things that effect Rx signal strength. For a PI_ Tx width, Tx shape(constant current or constant rate), Tx peak current, target size, target distance, target shape and orientation are some. Any others? Eric suggested optimum Tx width awhile back. Need more on Tx width or does anyone have a preference for the next topic? Include VLF in the discussion?}

[green]

For Fixed-inductance: Calculate Voltage output = 12000 * Gauss²* (200/coil-size) [coil-size in mm diameter]

For fixed-turns: Calculate Voltage output = 12000 * Gauss^{2 (from reply #168}

^{Coil diameter is just one of the things that effect Rx signal strength. For a PI_ Tx width, Tx shape(constant current or constant rate), Tx peak current, target size, target distance, target shape and orientation are some. Any others? Eric suggested optimum Tx width awhile back. Need more on Tx width or does anyone have a preference for the next topic? Include VLF in the discussion?}

Some thoughts, may or may not be correct. Keeping everything the same except.
double peak Tx current doubles Rx signal, maybe not signal/noise
increasing turns to double inductance doubles Rx signal, maybe not signal/noise
Rx signal is maximum when Tx width is greater than 5 times target time constant
For same average Tx current, constant rate Tx gives a higher Rx signal than constant current Tx
For same peak Tx current, constant current Tx gives a higher Rx signal then constant rate Tx

The chart could be used to estimate increase in detection distance if Rx signal is doubled and noise signal stayed the same. Increase for a small nugget at 3inches would be less than a US nickel at 16inches.

[Skippy]

As stated, the maths we've arrived at, can all be done in Excel.

The 'geometry' part of the Gauss formula's is as previously posted. All that is needed is the appropriate scaling coefficient to fit the figures to your existing tables/charts.
Again, I am going to assume a reference of V = 12000 for a 200mm diameter. coil, at target distance Z = 0.

Constant inductance:

V = 12 * R³ / ( Z² + R² )³
or: V = 12 * ( R / ( Z² + R² ))³


Constant Turns:

V = 120 * R⁴ / ( Z² + R² )³

.........

This should make it easy to evaluate a wider range of coil sizes. The nugget test target data (for the 133/200/300 coils) showed where smaller coils are better. An Excel chart of 'nugget-suitable' coil sizes would be an interesting one ( to nugget hunters, anyway !)

[Ferric Toes]

The following will help to explain the graph method of coil size and object range that I advocated in the past. This is part of a series of papers written by John Alldred, an Oxford physicist that I employed from 1970 - 1975 for a particular project involving mine clearance. He rewrote a lot of the basic theory on pulse induction that had been developed in the 1950's by F. B. Johnson. Sadly John died in 2002 from lung cancer.

Eric.

[Skippy]

I was just going through the maths of the 'semi-circle curves' last night, and I'll post up a nice version of the chart when I've scanned it later.

For Fixed Inductance coils, we had:

Output, V = K * ( R / ( Z² + R² ))³

To see how detection distance varies with coil size, we need to fix the value V. Changing V will represent changing to a larger/smaller target.

If V is fixed, the 'cubed' term in the above expression is redundant, and the equation can be simplified to:

Constant = R / ( Z² + R² )

Let the constant be 1 / (2*A)

Then ( Z² + R² ) = 2*A*R

and so Z² = 2*A*R - R²

So for a given coil R, we can find out detection distance Z.

Though not obvious, this is actually a formula for a circle, of radius A

Proof:

( Z² + R² ) = 2*A*R

so R² - 2*A*R + Z² = 0

which can be written as: [ using (a - b)² = a² - 2ab + b² ]

( R - A )² - A² + Z² = 0

so: ( R - A )² + Z² = A²

which is the circle equation x² + y² = A², with an offset of A on the x axis.

To generate a family of curves, increase the A value in even steps, eg. 0.05, 0.10, 0.15 ...etc.
For example: A = 0.2 generates a curve showing a 0.2m radius coil detecting a given target at a maximum distance Z = 0.2m.

I assume this could be done with Excel, I've done it the traditional way.

[green]

The following will help to explain the graph method of coil size and object range that I advocated in the past. This is part of a series of papers written by John Alldred, an Oxford physicist that I employed from 1970 - 1975 for a particular project involving mine clearance. He rewrote a lot of the basic theory on pulse induction that had been developed in the 1950's by F. B. Johnson. Sadly John died in 2002 from lung cancer.

Eric.

[ATTACH]42625[/ATTACH] [ATTACH]42626[/ATTACH] [ATTACH]42627[/ATTACH]

It's been 59 years since I had a math class so I'm slow with formulas. Did notice a statement in the second attachment under "Physical Dimensions of the Coil" about keeping inductance constant.

[Skippy]

It's a shame I can't attach the chart to my previous post, but here it is.

It's for circular PI mono coils, with a fixed inductance value. Coil radius, R is on the horizontal axis, Target distance Z on the vertical axis.

As all the curves are the same shape, the same chart can be re-scaled for larger or smaller dimensions. Example: if you're wanting a curve for a 0.05m radius coil, just multiply the radius and the target distances by 4, and use the R = 0.2 curve.

The chart is scanned at 200 DPI, so should print out OK on A4 paper. Total image size is about 1300 x 1300 pixels.

[green]

It's a shame I can't attach the chart to my previous post, but here it is.

It's for circular PI mono coils, with a fixed inductance value. Coil radius, R is on the horizontal axis, Target distance Z on the vertical axis.

As all the curves are the same shape, the same chart can be re-scaled for larger or smaller dimensions. Example: if you're wanting a curve for a 0.05m radius coil, just multiply the radius and the target distances by 4, and use the R = 0.2 curve.

The chart is scanned at 200 DPI, so should print out OK on A4 paper. Total image size is about 1300 x 1300 pixels.

Put both charts(fixed inductance) on same page. Both give the same results, detection distance vs coil size. Both assume everything remains the same but coil radius(diameter) and noise level doesn't change. Don't need math to chart the left chart. Been trying to understand the best way to use the left chart. With the Excel chart I can read change in signal strength or detection distance when changing coil size. Haven't figured how to read change in signal strength with the left chart.

[Skippy]

You can't read off signal strength from the semi-circle chart, I'm not sure if Excel could be persuaded to create such a chart.

I presume the Excel curves are produced from Hyperphys data, so adding a 600mm diameter/ R = 0.30 curve isn't simple. That would be the obvious advantage of fully generating the numbers in Excel, you can change scales, add arbitrary lines etc.

Was there any particular type of chart you were wanting to see? It's probably something we could create in Excel.